Spray nozzles with spiral flow of fluid and method of constructing the same

ABSTRACT

Constructions and methods of designs of nozzles with logarithmic spiral flow are disclosed having ratios of nozzle parameters and the patternation index held within certain ranges which enable such nozzles to be constructed with a high degree of predictability and description of spray performance in terms of flow rate, spray cone angle, patternation index and frictional fluid losses, and in the construction of very small nozzles and/or nozzles for spraying highly viscous fluids.

United States Patent [191 Polnauer Nov. 13, 1973 SPRAY NOZZLES WITH SPIRAL FLOW OF FLUID AND METHOD OF CONSTRUCTING THE SAME [76] Inventor: Frederick F. Polna uer, 250

Riverside Dr., New York, N.Y. 10025 22 Filed: Mar. 17, 1971 211 Appl. No.: 125,320

[52] US. Cl 239/468, 239/492 [51] Int. Cl B05b 1/34 [58] Field of Search 239/468, 492

[56] References Cited 5 UNITED STATES PATENTS Stanley 239/492 X 6/1967 Wahlin ..239/468 10/1970 Polnauer ,.239/1 Primary ExaminerLloyd L. King AttorneyDarby & Darby [57] ABSTRACT Constructions and methods of designs of nozzles with logarithmic spiral flow are disclosed having ratios of nozzle parameters and the patternation index held within certain ranges which enable such nozzles to be constructed with a high degree of predictability and description of spray performance in terms of flow rate, spray cone angle, 'patternation index and frictional fluid losses, and in the construction of very small nozzles and/or nozzles for spraying highly viscous fluids.

66 Claims, 19 Drawing Figures PATENIEMnnsma 3.771.728

SHEET 1 tF a FIG. 1

FIG. 2

FIG. 5

2 7 Q l lx llf/ 32 FIG. 20

, -l6 4 |6-" W I K I 5 1 (I60 I v 3? 38 FIG. 6 300 32 7/ X FREDERICK BY ATTORNEYS PATENIEBRM 1 3 I975 SHEET 2 EF 4 Minimum 13 m: 3.771. 728

SHEET 3 EF 4 FIG. 9

L IS 59. L

SHEET l EF 4 PAIENTEU Ill]? 1 3 I913 FIG. 17

' of the invention, the pressure head of the fluid to be sprayed is efficiently and effectively converted into kinetic energy of rotation in a swirl chamber. Thus, the nozzles of the invention are capable of producing a cone-shaped spray of very fine droplets that are uniformly discharged from the nozzle.

BACKGROUND OF THE INVENTION The logarithmic spiral flow of a fluid in a swirl chamr ber represents a so-called plane combined vortex-sink flow. In practice the ideal case of this type of flow cannot be realized because of the confinement of the flow by the cylindrical side wall of the swirl chamber and also by its top and bottom confining walls which are perpendicular to the chamber central axis. However, the ideal case can be approximated to fairly high degree and this is the objective of the nozzles of this invention.

In a swirl chamber type of nozzle, the flow of fluid into the swirl chamber can be provided through one or a plurality of inlets. The use of a plurality of inlets increases the danger of nozzle clogging and disturbs the i flow by squeezing the circulating fluid bands, particularly at the inlet. Multiple inlets also increase the inner fluid friction and distort the shape of the spiral. All of these factors result in a decrease of atomizing energy in the nozzle and therefore impair nozzle Ofi ICICIICY. Because of the aforesaid disadvantages of multiple inlets, the single inlet nozzle has been proven to be the best solution in producinga logarithmic spiral flo'w with good axial symmetry, provided that certain dimensional conditions of the swirl chamber and the orifice plate are met.

It should be understood, however, that a'swirl chamber with a single inlet does not in every case produce an efficient, axial-symmetric flow. British Pat. No. 760,972 (Magyarlrecognizes the need fordesign criteria for a single inlet nozzle so that it can produce a flow with good axial symmetry. This patent states that this can be achieved by making the ratio of the inlet width B to the largest radius of the swirl chamber at the neighborhood of the inlet opening (R not larger than 2/9.

In my prior Pat. No. 3,532,271 it is disclosed that ratios of at least six parameters are of importance in obsional parameters of spray nozzles with logarithmic spiral flow are disclosed which enable such nozzles to be produced which have a high degree of ability for description and predictability of spray performance, i.e., weight flow rate, spray cone angle, patternation index and frictional fluid losses relating to droplet size of the spray. Such nozzles can be designed, according to the invention, on a more scientific basis rather than by the usual cut-and-try methods. In addition, certain novel methods and design criteria are also disclosed so by maintaining ratiosof nozzle parameters and the patternation index within predetermined ranges, the nozzles can be designed and constructed so as to reliably describe and predict spray performance.

It is an objectof this invention to provide a spray nozzle wherein the fluid flow characteristics approach the ideal case of a plane combined vortex and sink flow represented by a logarithmic spiral flow with good axial symmetry and a uniformly distributed atomized fluid forming a conical spray and wherein the energy losses through inner fluid and wall friction and particle impact are minimized.

Another object is to provide novel design criteria for the swirl chamber inlet passage to minimize hydrodynamic losses prior to the entering of the fluid into the swirl chamber.

A further object is to provide novel design criteria for v improving the efficiency of the region of the nozzle outlet orifice.

Still another object is to provide improved orifice outlet configurations for a spray nozzle.

An additional object is to provide a spray nozzle in which the swirl chamber is retained within the housing bore by means of a spring which also retains a filter.

Still another object is to provide novel design criteria for the construction of very small nozzles and of nozzles used for spraying highly viscous fluids.

Other objects and advantages of the present invention will become more apparent upon reference to the following specification and annexed drawings, in

which:

FIG. 1 is a longitudinal cross-sectional view through i the center of one embodiment, of the spray nozzle containing good axial symmetry of the flow, which corresponds to a low patternation index in this type of nozzle. The subject invention discloses and claims improvements in the construction and methods of design of the nozzles of my prior patent. This includes constructions and method of design which take into consideration the individual effects of the largest radius, inlet width and height of the swirl chamber. In addition an improved method is provided to describe and predict the patternation index, and thus, to minimize frictional fluid losses and decrease. the 'droplet size of the spray.

SUMMARY OF THE INVENTION structed according to the principles of the invention;

'FIGS. 2 and=2aare-top-plan views of different em-- bodiments of swirl chamber bodies of the nozzle shown in FIG. 1, whose inner walls are shaped according to an arcof a curve;

FIG. 3 is a top plan view of another swirl chamber body with an improved configuration for the swirl chamber inlet passage;

FIG. 4 is a top plan view of still another swirl chamber body with an improved configuration for the swirl chamber inlet passage;

FIG. 5 is a longitudinal cross-sectional view taken along line 5-5 of FIG. 2;

FIG. 6 is a cross-sectional'view tak n along line 6-6 of FIG. 2; I A

FIG. 7 is a top plan view of the upper portion of a nozzle housing and a swirl chamber body as shown in FIG. I;

FIG. 8 is a longitudinal cross-sectional view taken along line 88 of FIG. 7;

FIG. 9 is a longitudinal cross-sectional view through the center of one embodiment of the spray nozzle made according to my invention showing a filter, and a spring retaining both the swirl chamber and the filter within the nozzle housing;

FIGS. 10 through 17 are longitudinal cross-sectional views through the center of the upper portions of various embodiments of nozzle housings; and

FIG. 18 is a diagrammatic plan view of the vector diagram of the peripheral and radial flow velocity components of a stream line.

Referring to FIG. 1, a preferred embodiment of a spray nozzle constructed according to my invention comprises a housing 10 of stepped cylindrical shape with a male thread 11 formed at the rear portion of its outer diameter. The other end of housing 10 has a front end wall defining an outlet orifice 12. A bore 14 is formed in housing 10 behind orifice 12 and extends to the housings rear end. A swirl chamber body 16 is closely fitted into the front portion of the bore 14 with its outlet in communication with orifice 12. The inner wall of housing 10 is also formed with a female thread 18 at its rear portion concentric with the longitudinal axis of swirl chamber body 16. A plug 20 with a male thread 22 mating with threads 18 firmly holds the swirl chamber body 16 within the bore 14 of housing 10. A conduit (not shown) supplies fluid to the swirl chamber body 16 through an inlet bore 24 of plug 20.

FIG. 2 shows part of the details of the swirl chamber body 16. The outer shape of the body is generally cylindrical. A transverse wall 16a separates the chamber 36 in which the spray is formed from a lower chamber 37 which receives the fluid from the inlet bore 24. The fluid from bore 24 enters an inlet passage 30 of chamber 36 through a cutout'32 in the wall 16a of swirl chamber body 16 (see FIG. 6). As shown in FIG. 6, the flow path is indicated by arrow A and fluid passes upwardly through cutout 32 in the wall 16a of the swirl chamber body 16, continues horizontally through the inlet passage 30 and enters the swirl chamber 36 which has an inner wall 34. The inner side wall 34 defining the shape of chamber 36 is preferably shaped according to an outer turn of an arc of a curve. It has been found, in general, that a logarithmic-spirally shaped swirl chamber is preferable in efficiency to a circularly shaped chamber. But there are various conditions under which it would be sufficient to use a circular wall or a number of circular sections together approximating the shape of a logarithmic spiral.

In the nozzle being described, the outer wall 31 of inlet passage 30 of the swirl chamber body is tangential to the arc of the inner wall 34 of the swirl chamber 36 at the line -5 which defines an imaginary plane at the horizontal axis of the chamber. The fluid to be sprayed circulates in the chamber 36 whose inner wall 34 is in the shape of a logarithmic spiral. After circulation, the fluid is discharged through the outlet orifice 12, usually in the shape of a hollow cone which is shown by the dotted lines 13 in FIG. 1. After passing through the outlet orifice 12, which is axially symmetric with bore 14 of housing 10, the discharged fluid disintegrates into very fine droplets due to-the effect of the centrifugal force of the circulating fluid.

FIGS. 2 and 5 show three major dimensional parameters of this spray nozzle which affect the efficiency and effectiveness of its spray performance. They are the height (H) of the swirl chamber 36 from the bottom wall of chamber 36 to its top wall; the width (B) of the inlet 30 at the inlet opening into the swirl chamber 36 at the tip of the rib 38 formed by the inner wall 34 of the swirl chamber at the inlet into the chamber; and the largest radius (R of the swirl chamber wall 34. Another important dimension is the thickness (S) of the rib 38 at its top.

FIG. 2 also shows another critical dimension, the minimum length (m of the inlet passage 30, which is the length from. the horizontal axis 5-5 to the edge 30a of the horizontal bottom wall of the inlet 30. FIG. 2a shows the case where the rib 38 does not extend up to the horizontal axis 5-5. As seen in FIG. 2a, the dimension B is still between the tip of rib 38 and a point on the inner wall 34 reached by a line drawn horizontally from the rib tip to the wall. The dimension m is again from the axis line 55 to the edge 300. In both embodiments of FIGS. 2 and 20, it is preferred that m, should at least be equal to the inlet width B to minimize hydrodynamic losses at the inlet of the swirl chamber. The dimension m is the maximum length of the inlet passage 30, from the horizontal axis 55 back to the end of the outer wall 31 of the inlet passage.

In FIGS. 2 and 2a, the inner wall 33 defining one wall of the inlet passage 30 and one wall of rib 38 is generally straight. FIG. 3 shows another configuration of the inlet passage 30. Here the inner wall 41 defining one side of inlet passage 30 is formed of arcuate shape. The first portion of the arc has a radius of curvature R starting at the outer wall of the swirl chamber body 16 and extends toward horizontal axis 5-5. This arc tight ens at the inner wall 41 of the inlet passage to a radius of curvature R near the tip of rib 38, which is the exit of the inlet passage. It has been found that it is preferable for efficient spray performance that R be larger than R The outer wall 43 defining the other side of inlet passage 30 is shown as being straight and is preferably made tangential to the are formed by the inner side wall 34 of the swirl chamber body which defines the chamber 36. If the inner wall 34 of the chamber has the shape of a logarithmic spiral, the outer wall 43 of inlet 30 should be under the constant angle 0. (omega) of the logarithmic spiral.

FIG. 4 shows another configuration of inlet passage 30. It differs from the embodiment of FIG. 3 in that the outer wall 44 defining one side of inlet passage 30 is formed by an arc with a radius of curvature R For optimal flow conditions, the relation R R R should exist. If desired, the arcuate wall 44 can be a continuation of the are formed by the inner wall 34 of the swirl chamber body.

FIG. 7 is a top plan view of the upper portion of the nozzle of FIG. 1 and shows the outlet orifice 12 having a circular shape. Several of the dimensional parameters shown in FIGS. 2 and 2a are again shown. In addition, the parameter G is shown which is the distance from the center of the swirl chamber 36 to the inner edge of the tip of the rib. 38. The distance G is defined by G R (B+S).

FIG. 8 is a sectional view of FIG. 7 along line 8-8 in which two other major dimensional parameters are shown. These are the diameter D,,, of the outlet orifice 12 and the axial thickness L of the orifice between the top plane of the swirl chamber 36 and the top of the or ifice, which is the end of the effective portion of the orifice insofar as the formation of the spray cone is concerned. The cone angle 24: of the hollow spray cone formed by the fine droplets is also shown.

The contour 57 of the orifice inner surface between the exit of the swirl chamber, that is, the top plane of the swirl chamber, and the exit of the orifice may be a curved or a straight line. The plane of the lower face of orifice 12 is in-the shape of a circle which has a diameter D To minimize or avoid leakage and disturbance of the flow, the radius R of this circle should preferably be smaller than the distance G. E

FIG. 9 shows another embodiment of the invention which is particularly useful for fuel injection in com bustion chambers. The same reference numerals are used for similar parts, where applicable, as in FIG. 1. This embodiment provides means for a filter screen 50 which is brazed to a filter ring 52. Ring 52 is firmly pressed against the bottom of swirl chamber body 16 by a spring 54 which serves the dual purpose of retaining the swirl chamber body 16 in the bore 14 of the housing 1 and the filter ring 52 in a fixed position at the bottom of body 16. The spring 54 is seated on a collar 56 and a retaining snap ring 58 holds the collar 56 firmly in place. Spring 54 performs the function of plug 20 in the embodiment of FIG. 1, and may also be used to retain the swirl chamber body 16 in the housing bore 14 without the use of a strainer. I

In each of the embodiments of swirl chamber bodies shown in FIGS. 1-9, to construct and design spray nozzles with a logarithmic spiral fiow to spray fluids with a kinematic viscosity larger than ,two centistokes, it has been found that for most efficient operation with such highly viscous fluids the dimensional ratio B/R should remain within the limits In addition, abrupt changes in direction of the flow cre- I ates turbulence, which also causes losses. It has been found that the hydrodynamic losses at the outlet orifice spray. The total thickness L of the orifice is from the beginning of curve 57 at point 59 to the top 60 of the cylindrical portion of height P. The distance L corresponds to the thickness from a point in the same place where curve 57 starts, that is the bottom surface of the portion of the housing or' plate in which the orifice is formed, to the top 70 of the conical surface 61.

can be reduced and in some cases minimized by various configurations and methods of design subject invention.

FIG. 10 shows a sectional view of a fragment of the upper portion of housing 10 of FIG. 1 defining the orifice 12, or of a separate orifice plate such as described in my aforesaid patent. The inner orifice contour 57 at the bottom of the orifice adjacent the top plane of the swirl chamber is shown as an arc of a circle or of any suitable curve, such asa spiral. 'It starts upward from point 59 at the bottom surface 18 of the orifice, which is the top surface of the swirl chamber, or an orifice plate (not shown). Point 59 defines a circle with a diameter D in the plane of the lower face of orifice 12. A sharp corner at intersection 59 should be avoided. The curve 57 intersects with the actual orifice diameter D,,, at point 59a. The orifice continues upwardly in the shape of a straight cylinder with an axial length P having a flat top surface 60. The top surface 60 of the orifice at the top of cylindrical portion of height P, is shaped as a circle with a diameter D,,,,. It extends upwardly as a cone 61 starting from the periphery of this circle to the top surface 70 which is usually the top of the housing. The conical surface is provided to catch individual droplets and to prevent dripping of the according to the The nozzle .orifice of FIG. 11' is similar to that of FIG. 10, except that the cylindrical portion of height P has been omitted. Curve 57 terminates in the flat upper surface 60.

The embodiment of nozzle of FIG. 12 is also similar to that of FIG. 10. Here, however, the conical surface 61 starts directly at the orifice diameter D,,,. at the top of the cylindrical portion of height P. This configuration further improves the spray conditions.

The nozzle of FIG. 13 corresponds to that of FIG. 12. Here P equals zero, that is, there is no cylindrical portion of height P and the upward conical taper 61 starts at the end of curve 57.

For certain applications, particularly in the types of orifices shown in FIGS. 11 and 13, it has been found advantageous to roundoff the top corner edge of the orifice. This top corner edge would correspond to the point where curved surface 57 meets fiat surface 60 in FIG. 1 l and to where curved surface 57 meets the conical surface 61 in FIG. 13. The rounded top corner edge contour 62 is shown in FIGS. 14 and 15 as being an arc of a circle with a radius r,. It also can be any suitable curve. Except for the rounded corner 62, the nozzle of FIG. 14 corresponds to the nozzle of FIG. 11, and the nozzle of FIG. 15 corresponds to the nozzle of FIG. 13.

FIG. 16 shows another form of nozzle which corresponds to that of FIG. 14. Here, however, what corresponded to the flat top surface 60 in FIG. 14 has been made a depressed, or grooved, surface 65. The purpose of groove 65 is to collect straying droplets and to guide them along conical surface 61 outside of the effective portion of the spray cone. In this embodiment, the distance L is from the flat underside 18 ofthe member forming the orifice (top of the swirl chamber) to the top of rounded portion 62. The spray cone is effectively formed in this portion of the orifice;

FIG. 17 shows another'embodim'entof nozzle orifice whose portion between the lower surface 18 and the conical surface '61 is formed by two "co'nnected'curved contour sections 57 and 66. In this case, the two sections are portions of arcs of circles of respective radii r and r,, the former having a larger radius. Here the distance L is between the lower surface 18 and the point 71 at which the two sections 57 and '66 join each other. The surfaces 57 and 66 also could beportions of curves with r, r," their radii of curvature.

In each of the embodiments of orifices of FIGS. 10 through 17, both the-length of orifice L and the thickness of the cover or orifice plate L, are shown. The orifice length L is defined by the distance between the top surface of the swirl chamber, which is the lower surface of the orifice forming member, or the lower surface of the orifice plate to a point where the formation of the spray is complete. The thickness L, of the housing or cover plate member is measured from the lower surface 18 to the top surface 70. The orifice length L should be made as small as possible, to produce optimal spray performance. Ithas been found that lengths of L as small as 0.005 inch are preferable. Using an L of this extremely small length causes a conflict with the structural requirements of the housing or orifice plate, and could, if no other steps were taken, make it too weak to withstand structural stresses caused by. high fluid pressures. This problem has been minimized in the orifice configurations of FIGS. -17 by combining a very small orifice length L with a sufficiently large orifice plate thickness L so that both requirements for flow dynamics and structural strength can be met simultaneously.

To achieve the foregoing objectives of flow dynamics and structural strengths, the following limits of two ratios L /L and F'IL should be observed:

l. Range of L,/L:

K, L /L K where the approximate numerical values of K and K are 2. Range of P/L (orifices of FIGS. 10 and 12) K P/L K Approximate numerical values of K and K are:

(upper limit of P is equal L and lower limit of P is equal zero) Further preferred conditions are:

1n the embodiments of FIGS. 14 and 15, L is defined by the distance between the highest horizontal point of radius r and the lower surface 18 of the member forming the orifice. It is preferable that r, L.

In the embodiment of FIG. 17, if the radius of curvature r of the inner (lower) orifice surface portion 57 is being considered relative to the outer (upper) orifice radius r,, then, the orifice length L for any given r and r may be defined by the distance of the point where the radii r and r defining sections 57 and 66 intersect, from the bottom surface 18 of the member defining the orifice.

One objective of the present invention is to produce in a spray nozzle with a single inlet swirl chamber a type of flow which will approximate to a high degree the ideal case of a plane combined vortex and sink flow represented by a logarithmic spirally shaped flow with good axial symmetry. This is accomplished by using certain novel methods and design criteria described below for determining the dimensional parameters of this type of nozzle and by maintaining ratios of these parameters and also the patternation index within predetermined ranges. Nozzles designed in this manner ,will be highly predictable and describable in their performance in terms of flow rate, spray cone angle, patternation index and frictional flow losses relating to droplet size of the spray.

For the design of a nozzle with logarithmic spiral flow, the following criteria are usually specified by the purchaser of the nozzle: the actual weight flow rate Q of the fluid; the spray cone angle (2 I11), nozzle pressure drop A p), specific weight of the fluid 'y, or gamma), kinematic viscosity v, or nu), and the maximum patternation index 6 or delta).

For a given nozzle the properties of the design are as follows:

Q actual weight flow rate (lbs/hr) of fluid 2 111 spray cone included angle (degrees) 0,, volume flow rate (l/sec) A p nozzle pressure drop; i.e. the pressure differential between the nozzle inlet pressure and the ambi ent pressure at the nozzle orifice plane (lbs/in) y (gamma) specific gravity in relation to water at specified temperature 8 (delta) patternation index, the degree of uniform weight distribution of the spray v (nu) kinematic viscosity (centistokes) The method of designing and calculating the parameters for this type of nozzle differs somewhat from the previous method disclosed in my aforesaid patent in that it dispenses with the use of the coefficient of discharge. Instead, the specified actual weight flow rate Q is used. The following equations for the flow rate, cone angle and patternation index are based on swirl chambers with an inner side wall corresponding to wall 34 described in FIGS. 1-10, shaped according to a logarithmic spiral.

Using water as a reference fluid at room temperature and p.s.i. as a reference pressure drop (A p it was found that the flow rate Q can be related to the dimensional parameters D B,H and R all previously described, by an empirical equation which is as follows:

log Q b log D l7 log B,H b log R K K b, and b are positive real number constants and b is a negative real number constant. K is an intercept in the computer program. For pressure drops Ap different from the reference pressure drop of l00 p.s.i. (Ap Q for l00 p.s.i. must be multiplied by V Kpx/Kp Thus,

Q Qref V Apx/Ap Further, it was found that the spray cone angle Zrbref for the given reference pressure drop of lOO p.s.i. is related to the parameters D B,H and R, by another empirical equation:

log 2illref= a, log B,H/D a log R -la;, log H a K gz liaezs P9 liy a numbe constants and a are negative real number constants.

For both weight flow rate Q and spray cone angle 24:, for fluids other than water, suitable correction factors for density and viscosity must be applied. Equation (6) for the spray coneangle 2111 holds true for pressure drops from -1 00 to 200 p.s.i.; however, for other pressure drops, correction factors for 2th must be used.

It was additionally found that the patternation index (8) delta, for water, at pressure drops from l00 to 200 p.s.i. is related to the parametersD L, B, H and R, by an empirical equation:

K 5 c c and c are positive real number constants. c and c are negative real number constants. Suitable correction factors for fluids other than water for density,

where K b, and b are positive real number constants and b is a negative real number constant.

Equation (5) remains the same for circular chambers for converting results of equation (8) at the reference pressure to another pressure. A

For spray cone angle:

log 2th ref= a log BI-l/D a log R, a log H a J 198 B if? i are yssl tsqastasta nd K a1 and a a and a, are negative real number constants. For patternation index delta:

ji c8 and 09 are positive real numberconstants and c c and c are negative real number constants.

For the design of a nozzle with a given weight flow rate Q and a spray cone angle 2:11, and a logarithmic spiral swirl chamber, a transformation of equations (4) and (6), is required. For circular swirl chambers, a transformation of equations (8) and (9) is required. in both cases, the parameters B and R, are assumed and D and H are to be determined from equations. L is also assumed, but is only relevant for 'the determination of the patternation index delta.

For a logarithmic swirl chamber the transformation involves the following steps:

log B a log R,

follows:

log H (B, F(2|,b) A F(Q) )/(B1A2 A1132) The transformation for a circular swirl chamber is analogous.

If the actual pressure drop Ap is different from the reference pressure drop Ap then Q adjusted for actual Ap must be inserted into equation (11) and 21!; adjusted for actual Ap into equation (12).

Considering now another aspect of nozzle design, it is known that the flow in a single inlet swirl chamber develops a moment of velocity of Drall. To obtain maximum efficiency and effectiveness in nozzle performance, an optimal moment of velocity is sought. Referring to FIG. 18, this occurs when the streamlines form logarithmic spirals with their angle 9 remaining substantially constant from the inlet of the swirl chamber to the outlet orifice, i.e., good axial symmetry is being maintained. The Magyar British patent teaches that such an optimum condition can be obtained if the ratio B/R is not larger than 2/9. I have found that this is not the case. I have also found that the patternation index 8 is a sensitive indicator for the level of axial symmetry of the flow within the swirl chamber. More specifically, a low patternation index normally gives use to a nozzle with good axial symmetry.

Due to fluid friction, the Drall decreases while the flow progresses toward the central axis of the swirl chamber. It is important for the designer of the nozzle to minimize Drall losses. A method is shown below for calculating Drall losses. It should be recognized that the higher the remaining Drall at the orifice, the greater the centrifugal force in the spray cone and the finer the droplets.

The general method for calculating Drall losses has been known for sometime. To make it sufficiently accurate and practically-meaningful, it must be based on the premise that an axially symmetric flow exists in the swirl chamber. It further presupposes that the major dimensional parameters of the nozzle, and in particular D,,, and H, are accurately calculated. Prior to the introduction of my methods of designing this nozzle and the prediction of the-patternation index, previous methods of calculating and designing the nozzle failed to meet these two basic premises to permit use of the Drall calculation method with any reasonable degree of accuracy. Through the use of the invention disclosed herein,

the Drall calculation method becomes practically usable. u j

Heretofore, to' obtain'a practical method for calculating Drall losses, it was assumed that theboundary layer at the curvedlside wall of the swirlchamber was'very thin and could therefore be ignored. This is not true for fluids with higher viscosity. Unless this assumption is made, however, the calculation of Drall losses becomes impossible. The method explained herein uses the assumption and is, therefore, only an approximation.

i determine frictional fluid losses is quite significant.

There are two types of fluid friction to be considered. These are: (a) inner friction, due to shearing stress at the lateral planes of the circulating fluid bands; and (b) horizontal wall friction, occuring at the bottom wall of the swirl chamber and at the horizontal lower surface of the orifice plate or the member defining the orifice.

Considering inner friction, this type of Drall loss is calculated based on the following consideration. Taking a single stream line, the logarithmic spiral flow consists of two partial flows; as may be seen from the diagram in FIG. 18. One flow component is circulatory, indicated by a circle with the radius r and with a peripheral velocity C The other component is radially inward with a velocity C,. The spiral flow asymptotically approaches the inner circle with its radius r,-, which circle represents also the base of the air core of the nozzle.

At the inlet to the swirl chamber, r R

As seen from FIG. 18, C,/C tan6.

Therefore, B/2rrR tan 8.

For most practical cases one can take B/ZwR sin8 since sin8 tan8 for small angles.

For a frictional fluid, the Drall D (m /sec) at the inlet to the swirl chamber is:

A v/2'1r sin 8 Another constant C is expressed by C 0.434 (D /A 0.362 log (D,,/A,) 2 log r where, r R (3/2) and R D /2 Drall D, is the amount of Drall remaining from the frictionless Drall D, due to inner friction loss.

1) A,/O.434 2 log R, c 0.65 log(2R,,,. 0

The percentage Drall loss is:

ADi/Do (Do Di)/Do Considering now the horizontal wall friction, D is the amount of Drall remaining from the frictionless Drall D due to horizontal wall friction. [f the height of the swirl chamber H is large enough so that turbulent flow will exist, then the Drall ratio D /D may be expressed by:

n/ w (M Sins) m/ M/ m) 1+ 1 )tis usually 0.3 but changes with the Reynolds number.

However, if the height H is small so that a laminar flow can be assumed, another formula is to be used:

The percentage Drall loss is AD /D (D D,,,)/Do

The total Drall loss in percent is:

AD/D, total [(ADi/Do) (ADw/Do)]% and the available Drall D D AD total The complete procedure for designing a nozzle according to my invention is summarized below. For example, consider that a nozzle must be constructed with a given weight flow rate Q, a spray cone angle 21]; at a given pressure drop Ap, a maximum patternation index 8 at the same pressure drop, and a percentage total Drall loss, based on 1 kg/cm pressure drop, not to exceed a certain limit.

The design procedure which is described is based on test data obtained from water as the reference fluid at a reference pressure drop of p.s.i. at room temperature. As has been previously stated, the formulas (4) and (6) through (14) require corrections if fluids with densities and viscosities other than water are used; formulas (4) and (6) through (14) must also be corrected for pressure drops other than 100 p.s.i. The method is as follows, by referring to logarithmic-spiral chambers First Step Assume dimensions for L, B and R Second Step Calculate F(Q) from equation (11) and F (2 h) from equation (12).

Third Step Calculate D,,, from equation (13).

Fourth Step Calculate H from equation (14).

Fifth step Using equation (7), calculate delta. If it exceeds the specified limit, go back to first step, make new assump tions for L, B and R and repeat the second through fifth steps.

Sixth Step Using equation (15), calculate D C er Seventh Step Calculate A from tion (17).

Eighth Step T Usingequations (l8) and (19), calculate Drall loss due'to inner friction.

Ninth Step Using equations (20) or (21 depending upon whether turbulent or laminar flow at the inlet exists, and equation (22), calculate the Drall loss due to horizontal wall friction.

Tenth Step Using equation (23 calculate the total Drall loss. If it exceeds the specified limit, go back to first step, make new assumptions for B and R and repeat the second through the tenth steps until the desired results are obtained. 7 i

Each of the five dimensional parameters or independent variables D,,,, L, B, H and R, contained in the above-described method and its equations are important for the description, prediction and optimization of nozzle performance in terms of weight flow rate, spray cone angle, patternation index and Drall. Since there is considerable interaction occurring among these five equation (16) and C from equaparameters, the limits within 'which the individual equations set forth above will be applicable cannot be de- 13 scribed merely by giving ranges on each variable separately. However, by defining ranges'for the following nine dimensional ratios, the result can'be achieved that within these ranges all the equations of the foregoing method will be usable for accomplishing a primary objective of the invention, that is the description, prediction and optimization of nozzle performance in terms of weight flow rate, spray cone angle, patternation and Drall.

The following nine dimensional ratios and their ranges apply to swirl chambers with a logarithmicspirally shaped cylindrical side wall, or to a circular side wall, or to a side wall composed of circular cylinder sections.

0.20 (B/D 6.0 0.25 (H/D 20.0 0.050

0.150 (L/D,,,) 8.00 0.050 Dar/R 0.001 (EH/R 0.40 p

0.30 (H/L) 10.0 0.25 (H/B) 21.0 0.50

The ranges of the nine ratios specified in the above group of dimensional ratios were obtained in the following manner. As the first step, a number of experiments involving different nozzle combinations with varying combinations of parameters D L, B, H and R, are run and the weight flow rate and the spray cone angle are measured for each experiment. The second step comprises the selection and screening of significant parameters affecting the patternation index. Since this was already accomplished in connection with the disclosed material in my issued US. patent identified above, nine ratios were selected from those cited in the patent. All of these nine ratios were plotted on log-log paper, each separately against the coefficient of discharge and the spray cone angle. From the average trend lines of the data sets of the ratios, these ratios were found to be significant for their effects on the coefficient of discharge (respectively the weight flow rate) and on the spray cone: angle.

As the third step, from these" plots critical ranges were established within which the mathematical models and formulas devisedinthe fourth'step would be valid;

- As the'fourth step, mathematical models and formulas for describing, predicting and optimizing weight flow rate Q, spray cone angle 2rp,and patternation index delta were deviseduThese models and formulas are based on the individual and/or combined effects of the five dimensional parameters on Q, Zipand delta.

As the fifth step, these models and formulas were statistically analyzed in a computenand the most significant single parameters, and their linear and non-linear ratios and combinations thereof selected. After all nonsignificant combinations of parameters were eliminated, equations for describing, predicting and optimizing for Q, 2d: and delta were derived, resulting in equations (4), (6) and (7), respectively, for circular chamber equations (8), (9) and (10).

I claim:

l. A nozzle for spraying .a fluid comprising body means formed with an inlet passage for receiving the fluid to be sprayed and a bore, means forming a swirl chamber having a portion which is in the shape of an arc of a curve, said swirl chamber having an inlet opening for communication with said bore, and means forming an orifice having an outlet in communication with said swirl chamber, said nozzle having at a reference pressure drop AP, an actual flow rate Q which is related to D 3, B.H (nozzle inlet area) and R by the relationship: I

1. log Q b log D 2 b log B.H b log R K and a'spray angle (21p) in degrees which is related to D B, H and R by another relationship: 2, log 2ilrref =a log (EH/D 3) a log R a;, log

-H a log B j: Kw where O is the weight flow rate at the reference pressure drop;

D is the diameter of orifice means outlet;

B is the width of the tangential inlet close to the inlet opening of the swirl chamber; I H is the height of the swirl chamber;

R is the largest radius of the swirl chamber;

2111 is the spray cone angle at the reference pressure drop;

AP is the reference pressure drop of the nozzle;

and:

where b through b a through 11 Kg and Kw are real number constants. 2. A nozzle as in claim 1, wherein said swirl chamber has the shapesubstantially of a logarithmic spiral.

3. A nozzle as in claim 1, wherein the actual flow rate (Q) at a given pressure drop (AP) is related to the actual flow rate at the reference pressure drop (Q by:

4. A nozzle as in claim 1 in which the patternatio index delta at the reference pressure drop AP is described and predicted as follows: I

where c through c and K are real number constants; delta is the patternation index delta at the reference pressure drop; and

L is the thickness of the orifice means at its outlet. 5. A nozzle as in claim 4, wherein the actual flow rate (Q) at a given pressure drop (AP) is related to the actual flow rate at the reference pressure drop (Q by:

6. A spray nozzle comprising body'mean's formed with an inlet passage for receiving the fluid to be sprayed and a bore, swirl chamber means formed with an inlet and a portion having a side wall which is in the shape of an arc of a curve and an inlet opening for communication with the bore and the swirl chamber, the inlet opening having a portion which is generally tangentialto an arcuate portion of theswirl chamber at its inlet opening, means defining an orifice having anoutlet in communication with the swirl chamber, the ratio of the width of the inlet opening (B) to the largest radius (R of the swirl chamber being within the range 7. The nozzle as in claim 6 in combination with a source of fluid having a kinematic viscosity of at least two centistokes.

8. The method of constructing a spray nozzle comprising the steps of forming a body'with an inlet passage for receiving the fluid to be sprayed and a bore, forming a swirl chamber vhaving a portion which is in the shape of an arc of a curve and an inlet opening for communication with the bore and the swirl chamber, the inlet opening having a portion which is generally tangential to anarcuate portion of the swirl chamber at its inlet opening, forming an orifice having an outlet inn communication with the swirl chamber, and constructing the nozzle with the parameters D R, H and R where:

D is the diameter of the orifice means outlet; B is the width of the tangential inlet close to the inlet opening of the swirl chamber; H is the height of the swirl chamber; R,, is the largest radius of the swirl chamber so that the parameters have the ratios or 81 7 or 82 a sc 831 or sc 84 and wherein g, through g,, are positive real number constants, where g is less than g g and g 83 is less than g and g ,g is less than g 9. The method of claim 8, wherein the orifice diameter (D and the height of the swirl chamber (H) are constructed with the following dimensions:

g ar 2- Q l z- (Q))/( 2 1 z 1) where A,, A B and B are real number constants and where (Q) g Q z ogB b logR K H241) log 2\l1 (a,+a log B a log R K where a a b b Ka and Kw are real number constants.

10. The method of claim 8, wherein the nozzle is constructed with the following additional ranges of ratios of parameters:

131R 85 and H/B g where g and g are positive real number constants and g is less than g, through g and g,; is greater than g 11. The method according to claim-8, wherein the nozzle is constructed with the following additional ranges of ratios of parameters:

where g and g are positive real number constants and 3 is less than g, through g and g, is less than g 12. The method according to claim 11, wherein the nozzle is constructed with the following additional ranges of ratios of parameters:

H/L 8 and B/L 8 where i 85 is less than g through g and g through g 3 is less than 3 through g and g and g 3 is less than g through g g and g 3a is less than g g g and g g, is less than g g and g 3-, is less than 3 and g 32 is less than g 13. The method of claim 8, wherein the nozzle is constructed with the following additional ratio of parameters in the given range:

where g is a positive real number constant and 3 is less than g g, and g 14. The method according to claim 12, wherein the nozzle is constructed with the following additional ratio of parameters in the given range:

where g through g are positive real number constants and g is less than g through g and g through g g; is less than g through 3 and g g and g g is less than g through g g g and g g is less than g g g g and g g is less than g g g and g g is less than g g and g g-, is less than 82 and g g is less than g 15. The method according to claim 14, wherein the orifice diameter (D and the height of the swirl chamber (H) are constructed with the following dimensions:

where A,, A B and B are real number constants and where F(Q) log Q b logB b logR K F(2tl1) log 2 ll] (a +a log B a logR K where a a b b K and K 4, are real number constants. i

16'. The method according to claim 8, wherein the raties of parameters of the swirl chamber means and the orifice means of the nozzle are constructed with the following range of values: 7

B/D 6.0 H/D 20.0 n/R, 4.0 and D /R referenced back to water having an inlet gage pressure of p.s.i. at room temperature.

17. The method accordingv to claim 16, wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle are constructed with the following additional ranges of values:

referenced back to water having an inlet gage pressure of 100 psi. at room temperature.

18. The method according to claim 16, wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle are constructed with the following additional ranges of values:

H/L l and B/L 3 referenced back to water having an inlet gage pressure of 100 p.s.i. at room temperature.

19. The method according to claim 17, wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle are constructed with the following additional ranges of values:

H/L 10 and B/L 3 referenced back to water having an inlet gage pressure of 100 p.s.i. at room temperature.

21. The method according to claim 19, wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle are constructed with the following additional ranges of values:

referenced back to water having an inlet gage pressure of 100 p.s.i. at room temperature.

22. The method of determining parameters for a spray nozzle of the type having at least body means formed with an inlet passage for receiving the fluid to be sprayed and a bore, swirl chamber means having a portion which is in the shape of a spiraland an inlet opening, said swirl chamber means also having an inlet means for communication between said bore and said inlet opening of said swirl chamber, said inlet means having a portion which is generally tangential to a portion of an arc of a curve of the swirl chamber at said inlet opening and orifice means having an outlet in communication with said swirl chamber, said nozzle when operating also having an actual flow rate (Q) which is related to a function of (D3,, B,H,R, and a 23. A nozzle for spraying a fluid comprising body means formed with an inlet passage for receiving the fluid to be sprayed and a bore, means forming a swirl chamber having at least a portion which is in the shape of a circle,said swirl chamber having an inlet opening for communication with said bore, and mean forming an orifice having an outlet in communication with said swirl chamber, said nozzle having at a reference pressure drop AP an actual flow rate O which is related to DJ, B.H. (nozzle inlet area) and R, by the relationship:

log 0 b, log 0 +5 log BH b 10g R K,

and a spray angle (211:) in degrees which is related to spray cone arigle' (2) which is related to a function of erence pressure drop through the corresponding different nozzles, measuring the actual flow rate (Q) of each of the nozzles operated at the refer ence pressure drop, measuring the spray coneangle (241) of the different nozzles at the reference pressure drop; and producing by machine from the measurements made the functions f and f of the following equations:

log Q b, log D b log B-H- b log R K log 2 4, -a log an o a, log R a, log H a.,logB+K q,

D B, H, and R by another relationship:

where Q is the weight flow rate at the pressure drop; D is the diameter of orifice means outlet; B is the width of the tangential inlet'close to the inlet opening of the swirl chamber; H is the height of the swirl chamber; R is the largest radius of the swirl chamber; 2w is the spray cone angle at the pressure drop; where K b and b are positive real number constants and b is a negative real number constant;

n Y J where K a and a are positive real number constants and a and a are negative real number constants. I 24. A nozzle as in claim 23 in which the patternation index delta (8) at a pressure drop Ap is described and predicted as follows: Y

g 5 C6 0% V ar) 1 or) s 9 63) C10 af/ 03+ K where c and K are real numberconstants; c c and c are negative real number constants; and L is the thickness of the orifice means at its outlet.

25. A spray nozzle comprising a body formed with an inlet passage for receiving the fluid to be'sprayed and a bore, a swirl chamber having a portion which is in the shape of an arc of a curve and an inlet opening for communication with the bore and the swirl chamber, the inlet opening having a portion which is generally tangential to anarcuate portion of the swirl chamber at its inlet opening, forming an orifice having an outlet in communication with the swirl chamber, said nozzle having the parameters D B, H and R where:

D',, is the diameter of the orifice means outlet;

B is the width of the tangentialinlet close to the inlet opening of the swirl chamber;

H is the height of the swirlchamber;

R is the largest radius of the swirl chamber with the parameters having the following ratios:

or g1, ar g2, l sc g aa brl sc g4 and wherein g through g are positive real number constants, where g,, is less than g g and g 8 is less than g and g g is less than g 26. A nozzle according to claim 25, wherein the orifice diameter (D,,,.) and the height of the swirl chamber (H) have the following dimensions:

log D where A,, A B and B are real number constants and where F(Q) log Q b logB b logR K F(2il1) log 24; (a,+a log B a log R K where a a b b KQ and are real number constants. I

27. A nozzle according to claim 25, wherein the nozzle has the following additional ranges of ratios of parameters:

where g and g are positive real number constants and g is less than g through g and g is greater than g 28. A nozzle according to claim 25, wherein the nozzle has the following additional ranges of ratios of parameters:

where g and g are positive real number constants and g is less than g. through g and g is less than 3 29. A nozzle according to claim 28 wherein the nozzle has the following additional ranges of ratios of parameters:

H/L g and-BIL 88 where g is a positive real number constantand g is less than g g and g 31. A nozzle as in claim 29 having the following the following additional ratio of parameters in the given range:

where i g through 8 are positive real number constants and g is less than g, through 34 and g through g g is less than g through g and g g and g 88 is less than g through g g g, and g g is less than g g g g and g g is less than g g g and g g is less than g g and g g is less than g and g g is less than g 32. A nozzle according to claim 31 wherein the orifice diameter (D,,,) and the height of the swirl chamber (H) have the following dimensions:

where A A B and B are real number constants and where F(Q) log Q b logB b logR K,

where a a b b IQ; and Kw are real number constants. V i

33. A nozzle as in claim 25 wherein the ratios of parameters of the ,swirl chamber means and the orifice means of the nozzle have the following range of values:

B/D 6.0 11/0,, 20.0 H/R" 4.0 and DM/R 3.0

referenced back to water having an inlet gage pressure of p.s.i. at room temperature.

34. A nozzle as in claim 33 wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle have the following additional ranges of values:

B-H/R, 0.4 and 11/8 21 referenced back to water having an inlet gage pressure of 100 p.s.i. at room temperature.

35. A nozzle as in claim 33 wheein the ratios of parameers of the swirl chamber means nd the orifice means of the nozzle have the following additional ranges of values:

referenced back to water having an inlet gage pressure of 100 p.s.i. at room temperature.

36. A nozzle as in claim 34 wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle have the following additional ranges of values:

H/L 10 and B/L 3 referenced back to water having an inlet gage pressure of 100 p.s.i. at. room temperature.

37. A nozzleas in claim 33 wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle have the following additional ranges of values:

referenced back to water having an inlet gage pressure of lOO p.s.i. at room temperature.

38. A nozzle as in claim 36 wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle have the following additional ranges of values:

LID, 8

referenced back to water having an inlet gage pressure of 100 psi. at room temperature.

39. The method of determining parameters for a spray nozzle of the type having body means formed with an inlet passage for receiving the fluid to be sprayed and a bore, swirl chamber means having at least a portion of which is in the shape of a circle and an inlet opening, said swirl chamber means also having an inlet means for communication between said bore and said inlet opening of said swirl chamber, said inlet means having a portion which is generally tangential to a portion of an arc of a curve of the swirl chamber at said inlet opening and orifice means having an outlet in communication with said swirl chamber, said nozzle when operating also having an actual flow rate (O) which is related to a function of D B,H,R, and a spray cone angle (24,) which is related to a function of (B-H/D, B,H,R, where:

D is the diameter of the orifice means outlet;

B is the width of the tangential inlet close to the inlet opening of the swirl chamber;

H is the height of the swirl chamber;

R,, is the largest radius of the swirl chamber; comprising the steps of operating a plurality of nozzles having different D B,H and R parameters at a reference inlet fluid pressure which produces a reference pressure drop through the corresponding different nozzles, measuring the actual flow rate (Q) of each of the nozzles operated at the reference pressure drop,

measuring the spray cone angle (24;) of the different nozzles at the reference pressure drop; and

producing by machine from the measurements made the functions f and f of the following equations:

Q 1;, log 1),, b log 'BH b, log R, n

and a spray angle (24:) in degrees which is related to D B, H, and R by another relationship:

log 2d; a, log (EH/D a log R 0 log H a log B Kw.

40. A method according toclaim 22 further comprising the step of producing by machine from the measurements made the function f; the following equa-- tions: a

42. A nozzle for spraying a fluidcomprising body means formed within an inlet passage for receiving the fluid to be sprayed and a bore, means forming a swirl chamber having a portion which is in the shape of an arc of a curve, said swirl chamber having an inlet opening for communication with said bore, and means forming a generally circular orifice having an outlet in communication with said swirl chamber, the lower surface of said orifice forming means having the shape of a portion of an arc of a curve starting from a point at the top plane of the swirl chamber and extending upwardly to form the nozzle outlet, the outer surface of the orifice tapering outwardly in a generally conical shape above the terminus of the curve of the orifice lower surface, the height of the orifice forming means from the upper plane of the swirl chamber to the terminus of the curved portion being L and the height from the upper plane of the swirl chamber to the top of the conical surface being L,, the ratio of L IL being in the range of K L K 43'. A nozzle as in claim 42 wherein the outer surface of said orifice forming means is generally horizontal between the terminus of said cylindrical portion and the beginning of generally conical surface.

44. A nozzle as in claim 42 wherein said generally conical surface of said orifice forming means commences at the terminus of the curved lower surface portion. v

45. A nozzle as in claim 42 wherein the terminus of the curved lower surface portion of said orifice forming means is connected to the start of said generally conical surface by a substantially horizontal surface portion.

46. A nozzle as in claim 42, wherein said curved portion has at least first and second curvatures whose rspective radii are different.

47. A nozzle as in claim 46, wherein the terminusof said curved portion is connected to the beginning of the generally conical surface by a depressed groove portion whose height is lower than that of the highest point of the curved surface.

48. A nozzle as in claim 46, wherein the terminus of said curved portion is joined directly to the beginning of the generally conical surface. I

49. A nozzle for spraying a fluid comprising body means formed withinan inlet passage for receiving the fluid to be sprayed and a bore, means forming a swirl chamber having a portion which is in the shape of an arc of a curve, said swirl chamber having an inlet opening for communication with said bore, and means forming a generally circular orifice having an outlet in communication with said swirl chamber, the lower surface of said orifice forming means having the shape of a portion of an arc of curve starting from a point at the top plane of the swirl chamber and extendingupwardly to form the nozzle outlet, the outer surface of the orifice tapering outwardly in a generally conical shape above the terminus of the curve of the orifice lower surface, said orifice forming means having a cylindrical surface between'the terminus of the curve of said lower surface and the generally conical outer surface, the height of the orifice. forming means from the upper plane of the swirl chamber to the upper point of the cylindrical suris L, the height of said cylindrical portion being P and the range of P/L being K P/L l(,.

51. A nozzle as in claim 59, wherein K, 2 and K 52. A nozzle as in claim 42, wherein K, 2 and K 53. A nozzle as in claim 49, wherein K 2 and K 54. A nozzle as in claim 23, wherein said chamber has a portion in the shape of a cylinder.

55. A nozzle as in claim 50 wherein k 0.001 and 56. A nozzle as in claim 50 wherein the limit of P 57. A nozzle as in claim 56 wherein k 0.001 and 58. A nozzle as in claim 50 wherein k k and 59. A nozzle as in claim 58 wherein k 0.001 and 60. A nozzle as in claim 42 wherein a depressed groove portion is formed between the terminus of the curve of the orifice lower surface and the beginning of the conical surface.

61. A nozzle for spraying a fluid comprising body means formed within an inlet passage for receiving the fluid to be sprayed and a bore, means forming a swirl chamber having a portion which is in the shape of an arc of a curve, said swirl chamber having an inlet opening for communication with said bore, and means forming a generally circular orifice having an outlet in communication with said swirl chamber, the lower surface of said orifice forming means having the shape of a portion of an arc of a curve starting from a point at the top plane of the swirl chamber and extending upwardly to form the nozzle outlet, the outer surface of the orifice tapering outwardly in a generally conical shape above the terminus of the curve of the orifice lower surface, the height of the orifice forming means from the upper plane of the swirl chamber to the terminus of the curved portion being L, and the radius of the curved portion being r, with r being less than L.

62. A nozzle as in claim 61 wherein the surface from the top plane of the swirl chamber to the beginning of the conical surface is fully curved and has two different means formed with an inlet passage for receiving the fluid to be sprayed and a bore, means forming a swirl chamber having at least a portion which is in the shape of a circle, said swirl chamber having an inlet opening for communication with said bore, and means forming an orifice having an outlet in communication with said swirl chamber, said nozzle having at a reference pressure drop AP, an actual flow rate Q which is related to DJ, 8.11 (nozzle inlet area) and R by the relationship:

log Or y b log D b log BH b log R K and a spray angle (21!!) in degrees which is related to D or, B, H and R, by another relationship:

log 2rp a log (Bl-l/D a log R a log H+a log B K where Q is the weight flow rate at the reference pressure drop;

D, is the diameter of orifice means outlet;

B is the width of the tangential inlet close to the inlet opening of the swirl chamber;

H is the height of the swirl chamber;

R is the largest radius of the swirl chamber;

2111 is the spray cone angle at the reference pressure drop;

AP, is the reference pressure drop of the nozzle;

and:

where b.; through b a through as, K and K are I the real number constants.

64. A nozzle as in claim 63 wherein the actual flow rate (Q) at a given pressure drop (AP) is related to the actual flow rate at the reference pressure drop (0 by:

Q Qref T!- 65. A nozzle as in claim 63 in which the patternation index delta at the reference pressure drop AP is described and predicted as follows:

log 8 te; 6 8 w or] A /Do.)

8 or) 9 l or) 10 sc or) 5 where 0 through c and K are real number constants; delta is the patternation index delta at the reference pressure drop; and L is the thickness of the orifice means at its outlet.

66. A nozzle as in claim 65, wherein the actual flow rate (Q) at a given pressure drop (AP) is related to the actual flow rate at the reference pressure drop (Q by:

Q Qyef V AP/AP 

1. A nozzle for spraying a fluid comprising body means formed with an inlet passage for receiving the fluid to be sprayed and a bore, means forming a swirl chamber having a portion which is in the shape of an arc of a curve, said swirl chamber having an inlet opening for communication with said bore, and means forming an orifice having an outlet in communication with said swirl chamber, said nozzle having at a reference pressure drop Delta Pref an actual flow rate Qref which is related to Dor2, B.H (nozzle inlet area) and Rsc by the relationship:
 1. log Qref b1 log Dor 2 + b2 log B.H - b3 log Rsc + KQ and a spray angle (2 psi ) in degrees which is related to D2 or, B, H and Rsc by another relationship:
 2. log 2 psi ref -a1 log (BH/Dor2) + a2 log Rsc + a3 log H - a4 log B + K2 where Qref is the weight flow rate at the reference pressure drop; Dor is the diameter of orifice means outlet; B is the width of the tangential inlet close to the inlet opening of the swirl chamber; H is the height of the swirl chamber; Rsc is the largest radius of the swirl chamber; 2 psi ref is the spray cone angle at the reference pressure drop; Delta Pref is the reference pressure drop of the nozzle; and: where b1 through b3, a1 through a4, KQ and K2 are real number constants.
 2. log 2 psi ref -a1 log (BH/Dor2) + a2 log Rsc + a3 log H - -a4 log B + K2 where Qref is the weight flow rate at the reference pressure drop; Dor is the diameter of orifice means outlet; B is the width of the tangential inlet close to the inlet opening of the swirl chamber; H is the height of the swirl chamber; Rsc is the largest radius of the swirl chamber; 2 psi ref is the spray cone angle at the reference pressure drop; Delta Pref is the reference pressure drop of the nozzle; and: where b1 through b3, a1 through a4, KQ and K2 are real number constants.
 2. A nozzle as in claim 1, wherein said swirl chamber has the shape substantially of a logarithmic spiral.
 3. A nozzle as in claim 1, wherein the actual flow rate (Q) at a given pressure drop ( Delta P) is related to the actual flow rate at the reference pressure drop (Qref) by:
 3. Q Qref Square Root Delta P/ Delta Pref
 4. A nozzle as in claim 1 in which the patternation index deltaref at the reference pressure drop Delta Pref is described and predicted as follows: log deltaref -c1log (LBH3/Rsc Dor4-c2(B/Dor) + c3(H/Dor) + c4(B2/D2or) + +c5(L2/Dor2) + K where c1 through c5 and K are real number constants; deltaref is the patternation index delta at the reference pressure drop; and L is the thickness of the orifice means at its outlet.
 5. A nozzle as in claim 4, wherein the actual flow rate (Q) at a given pressure drop ( Delta P) is related to the actual flow rate at the reference pressure drop (Qref) by: Q Qref Square Root Delta P/ Delta Pref
 6. A spray nozzle comprising body means formed with an inlet passage for receiving the fluid to be sprayed and a bore, swirl chamber means formed with an inlet and a portion having a side wall which is in the shape of an arc of a curve and an inlet opening for communication with the bore and the swirl chamber, the inlet opening having a portion which is generally tangential to an arcuate portion of the swirl chamber at its inlet opening, means defining an orifice having an outlet in communication with the swirl chamber, the ratio of the width of the inlet opening (B) to the largest radius (Rsc) of the swirl chamber being within the range 1/4.5 < (B/Rsc) < (1/1.2)
 7. The nozzle as in claim 6 in combination with a source of fluid having a kinematic viscosity of at least two centistokes.
 8. The method of constructing a spray nozzle comprising the steps of forming a body with an inlet passage for receiving the fluid to be sprayed and a bore, forming a swirl chamber having a portion which is in the shape of an arc of a curve and an inlet opening for communication with the bore and the swirl chamber, the inlet opening having a portion which is generally tangential to an arcuate portion of the swirl chamber at its inlet opening, forming an orifice having an outlet inn communication with the swirl chamber, and constructing the nozzle with the parameters Dor, R, H and Rsc, where: Dor is the diameter of the orifice means outlet; B is the width of the tangential inlet close to the inlet opening of the swirl chamber; H is the height of the swirl chamber; Rsc is the largest radius of the swirl chamber so that the parameters have the ratios B/Dor < g1 , H/Dor < g2 , H/Rsc < g3, Dor/Rsc < g4 and wherein g1 through g4 are positive real number constants, where g4 is less than g1, g2 and g3 g3 is less than g1 and g2 g1 is less than g2
 9. The method of claim 8, wherein the orifice diameter (Dor) and the height of the swirl chamber (H) are constructed with the following dimensions: log Dor (B2. F(2 psi ) -A2. F(Q))/(B2A1-A2B1) 1 log H (B1.F(2 psi ) -A1F(Q))/(B1A2- A1B 2) 2 where A1, A2, B1 and B2 are real number constants and where F(Q) log Q - b2logB - b3logRsc - KQ 3 F(2 psi ) log 2 psi -(a1+a2) log B - a2log Rsc - K2 4 where a1, a2, b2, b3, KQ and K2 are real number constants.
 10. The method of claim 8, wherein the nozzle is constructed with the following additional ranges of ratios of parameters: B./Rsc < g5 and H/B < g6 where g5 and g6 are positive real number constants and g5 is less than g1 through g4 and g6 is greater than g2.
 11. The method according to claim 8, wherein the nozzle is constructed with the following additional ranges of ratios of parameters: H/L < g7 and B/L < g8 where g7 and g8 are positive real numBer constants and g8 is less than g1 through g3 and g7 is less than g2.
 12. The method according to claim 11, wherein the nozzle is constructed with the following additional ranges of ratios of parameters: H/L < g7 and B/L < g8 where g5 is less than g1 through g4 and g6 through g8 g4 is less than g1 through g3 and g6 and g7 g8 is less than g1 through g3, g6 and g7 g3 is less than g1, g2, g6 and g7 g1 is less than g2, g6 and g7 g7 is less than g2 and g6 g2 is less than g6
 13. The method of claim 8, wherein the nozzle is constructed with the following additional ratio of parameters in the given range: L/Dor < g9 where g9 is a positive real number constant and g9 is less than g2, g6 and g7.
 14. The method according to claim 12, wherein the nozzle is constructed with the following additional ratio of parameters in the given range: L/Dor < g9 where g1 through g9 are positive real number constants and g5 is less than g1 through g4 and g6 through g9 g4 is less than g1 through g3 and g6, g7 and g9 g8 is less than g1 through g3, g6, g7 and g9 g3 is less than g1, g2, g6, g7 and g9 g1 is less than g2, g6, g7 and g9 g9 is less than g2, g6 and g7 g7 is less than g2 and g6 g2 is less than g6
 15. The method according to claim 14, wherein the orifice diameter (Dor) and the height of the swirl chamber (H) are constructed with the following dimensions: log Dor (B2.F(2 psi ) -A2.F(Q))/(B2A1-A2B1)
 1. log H (B1.F(2 psi ) -A1F(Q))/(B1A2-A1B2)
 2. where A1, A2, B1 and B2 are real number constants and where F(Q) log Q - b2logB - b3logRsc - KQ
 3. F(2 psi ) log 2 psi -(a1+a2) log B - a2logRsc - K2
 4. where a1, a2, b2, b3, KQ and K2 are real number constants.
 16. The method according to claim 8, wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle are constructed with the following range of values: B/Dor < 6.0 H/Dor < 20.0 H/Rsc < 4.0 and Dor/Rsc < 3.0 referenced back to water having an inlet gage pressure of 100 p.s.i. at room temperature.
 17. The method according to claim 16, wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle are constructed with the following additional ranges of values: B.H/Rsc < 0.4 and H/B < 21 referenced back to water having an inlet gage pressure of 100 p.s.i. at room temperature.
 18. The method according to claim 16, wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle are constructed with the following additional ranges of values: H/L < 10 and B/L < 3 referenced back to waTer having an inlet gage pressure of 100 p.s.i. at room temperature.
 19. The method according to claim 17, wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle are constructed with the following additional ranges of values: H/L < 10 and B/L < 3 referenced back to water having an inlet gage pressure of 100 p.s.i. at room temperature.
 20. The method according to claim 16, wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle are constructed with the following additional ranges of values: L/Dor < 8 referenced back to water having an inlet gage pressure of 100 p.s.i. at room temperature.
 21. The method according to claim 19, wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle are constructed with the following additional ranges of values: L/Dor < 8 referenced back to water having an inlet gage pressure of 100 p.s.i. at room temperature.
 22. The method of determining parameters for a spray nozzle of the type having at least body means formed with an inlet passage for receiving the fluid to be sprayed and a bore, swirl chamber means having a portion which is in the shape of a spiral and an inlet opening, said swirl chamber means also having an inlet means for communication between said bore and said inlet opening of said swirl chamber, said inlet means having a portion which is generally tangential to a portion of an arc of a curve of the swirl chamber at said inlet opening and orifice means having an outlet in communication with said swirl chamber, said nozzle when operating also having an actual flow rate (Q) which is related to a function of (D2or, B,H,Rsc), and a spray cone angle (2 psi ) which is related to a function of (B.H/D2or, B,H,Rsc) where: Dor is the diameter of the orifice means outlet; B is the width of the tangential inlet close to the inlet opening of the swirl chamber; H is the height of the swirl chamber; Rsc is the largest radius of the swirl chamber; comprising the steps of operating a plurality of nozzles having different Dor, B,H and Rsc parameters at a reference inlet fluid pressure which produces a reference pressure drop through the corresponding different nozzles, measuring the actual flow rate (Q) of each of the nozzles operated at the reference pressure drop, measuring the spray cone angle (2 psi ) of the different nozzles at the reference pressure drop; and producing by machine from the measurements made the functions f1 and f2 of the following equations: log Q b1 log Dor2 + b2 log B.H - b3 log Rsc + KQ
 1. log 2 psi -a1log (B.H/Dor2) + a2 log Rsc + a3 log H - -a4 log B + K2 .
 2. 23. A nozzle for spraying a fluid comprising body means formed with an inlet passage for receiving the fluid to be sprayed and a bore, means forming a swirl chamber having at least a portion which is in the shape of a circle, said swirl chamber having an inlet opening for communication with said bore, and mean forming an orifice having an outlet in communication with said swirl chamber, said nozzle having at a reference pressure drop Delta Pref an actual flow rate Qref which is related to Dor2, B.H. (nozzle inlet area) and Rsc by the relationship: log Q b4 log Dor2 + b5 log BH + b6 log Rsc + KQ
 1. and a spray angle (2 psi ) in degrees which is related to D2or, B, H, and Rsc by anotHer relationship: log 2 psi a5 log (BH/Dor2) + a6 log Rsc + a7 log H + a8 log B + K2
 2. where Q is the weight flow rate at the pressure drop; Dor is the diameter of orifice means outlet; B is the width of the tangential inlet close to the inlet opening of the swirl chamber; H is the height of the swirl chamber; Rsc is the largest radius of the swirl chamber; 2 psi is the spray cone angle at the pressure drop; where KQ, b4 and b5 are positive real number constants and b6 is a negative real number constant; and where K2 , a7 and a8 are positive real number constants and a5 and a6 are negative real number constants.
 24. A nozzle as in claim 23 in which the patternation index delta ( delta ) at a pressure drop Delta p is described and predicted as follows: log delta (delta) c6 log ((LBH3/Rsc Dor4) ) + c7 (B/Dor) + c8 (H/D) + c9 (B2/Dor2) + c10 (Rsc2/Dor2) + K . where c8, c9, and K are real number constants; c6, c7 and c10 are negative real number constants; and L is the thickness of the orifice means at its outlet.
 25. A spray nozzle comprising a body formed with an inlet passage for receiving the fluid to be sprayed and a bore, a swirl chamber having a portion which is in the shape of an arc of a curve and an inlet opening for communication with the bore and the swirl chamber, the inlet opening having a portion which is generally tangential to an arcuate portion of the swirl chamber at its inlet opening, forming an orifice having an outlet in communication with the swirl chamber, said nozzle having the parameters Dor, B, H and Rsc, where: Dor is the diameter of the orifice means outlet; B is the width of the tangential inlet close to the inlet opening of the swirl chamber; H is the height of the swirl chamber; Rsc is the largest radius of the swirl chamber with the parameters having the following ratios: B/Dor < g1 , H/Dor < g2 , H/Rsc < g3 , Dor/Rsc < g4 and wherein g1 through g4 are positive real number constants, where g4 is less than g1, g2 and g3 g3 is less than g1 and g2 g1 is less than g2
 26. A nozzle according to claim 25, wherein the orifice diameter (Dor) and the height of the swirl chamber (H) have the following dimensions: log Dor (B2.F(2 psi ) -A2.F(Q))/(B2A1-A2B1) 1 log H (B1.F(2 psi ) -A1F(Q))/(B1A2-A1B2)
 2. where A1, A2, B1 and B2 are real number constants and where F(Q) log Q - b2logB - b3logRsc - KQ 3 F(2 psi ) log 2 psi -(a1+a2) log B - a2log Rsc - K2 4 where a1, a2, b2, b3, KQ and K2 are real number constants.
 27. A nozzle according to claim 25, wherein the nozzle has the following additional ranges of ratios of parameters: B.H/Rsc < g5 and H/B < g6 where g5 and g6 are positive real number constants and g5 is less than g1 through g4 AND g6 is greater than g2.
 28. A nozzle according to claim 25, wherein the nozzle has the following additional ranges of ratios of parameters: H/L < g7 and B/L < g8 where g7 and g8 are positive real number constants and g8 is less than g1 through g3 and g7 is less than g2.
 29. A nozzle according to claim 28 wherein the nozzle has the following additional ranges of ratios of parameters: H/L < g7 and B/L < g8 where g5 is less than g1 through g4 and g6 through g8 g4 is less than g1 through g3 and g6 and g7 g8 is less than g1 through g3, g6 and g7 g3 is less than g1, g2, g6 and g7 g1 is less than g2, g6 and g7 g7 is less than g2 and g6 g2 is less than g6.
 30. A nozzle as in claim 8 wherein the nozzle has the following additional ratio of parameters in the given range: L/Dor < g9 where g9 is a positive real number constant and g9 is less than g2, g6 and g7.
 31. A nozzle as in claim 29 having the following the following additional ratio of parameters in the given range: L/Dor < g9 where i g1 through g9 are positive real number constants and g5 is less than g1 through g4 and g6 through g9 g4 is less than g1 through g3 and g6, g7 and g9 g8 is less than g1 through g3, g6, g7 and g9 g3 is less than g1, g2, g6, g7 and g9 g1 is less than g2, g6, g7 and g9 g9 is less than g2, g6 and g7 g7 is less than g2 and g6 g2 is less than g6.
 32. A nozzle according to claim 31 wherein the orifice diameter (Dor) and the height of the swirl chamber (H) have the following dimensions: log Dor (B2.F(2 psi ) -A2.F(Q))/B2A1-A2B1) 1 log H (B1.F(2 psi ) -A1F(Q))/(B1A2-A1B2) 2 where A1, A2, B1 and B2 are real number constants and where F(Q) log Q - b2logB - b3logRsc - KQ 3 F(2 psi ) log 2 psi -(a1+a2) log B - a2logRsc - K2 4 where a1, a2, b2, b3, KQ and K2 are real number constants.
 33. A nozzle as in claim 25 wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle have the following range of values: B/Dor < 6.0 H/Dor < 20.0 H/Rsc < 4.0 and Dor/Rsc < 3.0 referenced back to water having an inlet gage pressure of 100 p.s.i. at room temperature.
 34. A nozzle as in claim 33 wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle have the following additional ranges of values: B.H/Rsc < 0.4 and H/B < 21 referenced back to water having an inlet gage pressure of 100 p.s.i. at room temperature.
 35. A nozzle as in claim 33 wheein the ratios of parameers of the swirl chamber means nd the orifice means of the nozzle have the following additional ranges of values: H/L < 10 and B/L < 3 referenced back to water having an inlet gage pressure of 100 p.s.i. at room temperature.
 36. A nozzle as in claim 34 wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle have the following additional ranges of values: H/L < 10 and B/L < 3 referenced back to water having an inlet gage pressure of 100 p.s.i. at room temperature.
 37. A nozzle as in claim 33 wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle have the following additional ranges of values: L/Dor < 8 referenced back to water having an inlet gage pressure of 100 p.s.i. at room temperature.
 38. A nozzle as in claim 36 wherein the ratios of parameters of the swirl chamber means and the orifice means of the nozzle have the following additional ranges of values: L/Dor < 8 referenced back to water having an inlet gage pressure of 100 p.s.i. at room temperature.
 39. The method of determining parameters for a spray nozzle of the type having body means formed with an inlet passage for receiving the fluid to be sprayed and a bore, swirl chamber means having at least a portion of which is in the shape of a circle and an inlet opening, said swirl chamber means also having an inlet means for communication between said bore and said inlet opening of said swirl chamber, said inlet means having a portion which is generally tangential to a portion of an arc of a curve of the swirl chamber at said inlet opening and orifice means having an outlet in communication with said swirl chamber, said nozzle when operating also having an actual flow rate (Q) which is related to a function of D2or, B,H,Rsc), and a spray cone angle (2 psi ) which is related to a function of (B.H/D2or, B,H, Rsc) where: Dor is the diameter of the orifice means outlet; B is the width of the tangential inlet close to the inlet opening of the swirl chamber; H is the height of the swirl chamber; Rsc is the largest radius of the swirl chamber; comprising the steps of operating a plurality of nozzles having different Dor, B,H and Rsc parameters at a reference inlet fluid pressure which produces a reference pressure drop through the corresponding different nozzles, measuring the actual flow rate (Q) of each of the nozzles operated at the reference pressure drop, measuring the spray cone angle (2 psi ) of the different nozzles at the reference pressure drop; and producing by machine from the measurements made the functions f1 and f2 of the following equations: log Q b4 log Dor2 + b5 log BH - b6 log Rsc + KQ
 1. and a spray angle (2 psi ) in degrees which is related to D2or, B, H, and Rsc by another relationship: log 2 psi a5 log (BH/Dor2) - a6 log Rsc + a7 log H + a8 log B + K2 . 2
 40. A method according to claim 22 further comprising the step of producing by machine from the measurements made the function f3 the following equations: delta ( delta ) -c1 log ((LBH3/Rsc Dor4))- c2(B/Dor) + c3 (H/Dor) + c4 (B2/Dor2) + c5 (L2/Dor2) + K .
 41. A method according to claim 2 further comprising the step of producing by machine from the measurements made the function F3 of the following equation: log delta (delta) -c6 log ((LBH3/Rsc Dor4) - c7(B/Dor) + c8 (H/Dor) + c9(B2/Dor2) - c10 (Rsc2/Dor2) + K delta .
 42. A nozzle for spraying a fluid comprising body means formed within an inlet passage for receiving the fluid to be sprayed and a bore, means forming a swirl chamber having a portion which is in the shape of an arc of a curve, said swirl chamber having an inlet opening for communication with said bore, and means forming a generally circular orifice having an outlet in communication with said swirl chamber, the lower surface of said orifice forming means having the shape of a portion of an arc of a curve starting from a point at the top plane of the swirl chamber and extending upwardly to form the nozzle outlet, the outer surface of the orifice tapering outwardly in a generally conical shape above the terminus of the curve of the orifice lower surface, the height of the orifice forming means from the upper plane of the swirl chamber to the terminus of the curved portion being L and the height from the upper plane of the swirl chamber to the top of the conical surface being L1, the ratio of L1/L being in the range of K1 < L1/L < K2.
 43. A nozzle as in claim 42 wherein the outer surface of said orifice forming means is generally horizontal between the terminus of said cylindrical portion and the beginning of generally conical surface.
 44. A nozzle as in claim 42 wherein said generally conical surface of said orifice forming means commences at the terminus of the curved lower surface portion.
 45. A nozzle as in claim 42 wherein the terminus of the curved lower surface portion of said orifice forming means is connected to the start of said generally conical surface by a substantially horizontal surface portion.
 46. A nozzle as in claim 42, wherein said curved portion has at least first and second curvatures whose rspective radii are different.
 47. A nozzle as in claim 46, wherein the terminus of said curved portion is connected to the beginning of the generally conical surface by a depressed groove portion whose height is lower than that of the highest point of the curved surface.
 48. A nozzle as in claim 46, wherein the terminus of said curved portion is joined directly to the beginning of the generally conical surface.
 49. A nozzle for spraying a fluid comprising body means formed within an inlet passage for receiving the fluid to be sprayed and a bore, means forming a swirl chamber having a portion which is in the shape of an arc of a curve, said swirl chamber having an inlet opening for communication with said bore, and means forming a generally circular orifice having an outlet in communication with said swirl chamber, the lower surface of said orifice forming means having the shape of a portion of an arc of curve starting from a point at the top plane of the swirl chamber and extending upwardly to form the nozzle outlet, the outer surface of the orifice tapering outwardly in a generally conical shape above the terminus of the curve of the orifice lower surface, said orifice forming means having a cylindrical surface between the terminus of the curve of said lower surface and the generally conical outer surface, the height of the orifice forming means from the upper plane of the swirl chamber to the upper point of the cylindrical surface is L and the height from the upper plane of the swirl chamber to the top of the conical surface is L1, the ratio of L1/L being in the range of K1 < L1/L < K2.
 50. A nozzle as in claim 49 wherein the height of the orifice forming means from the upper plane of the swirl chamber to the upper point of the cylindrical surface is L, the height of said cylindrical portion being P and the range of P/L being K3 < P/L < K4.
 51. A nozzle as in claim 59, wherein K1 2 and K2
 100. 52. A nozzle as in claim 42, wherein K1 2 and K2
 100. 53. A nozzle as in claim 49, wherein K1 2 and K2
 100. 54. A nozzle as in claim 23, wherein said chamber has a portion in the shape of a cylinder.
 55. A nozzle as in claim 50 wherein k3 0.001 and k4 1.0.
 56. A nozzle as in claim 50 wherein the limit of P L.
 57. A nozzle as in claim 56 wherein k3 0.001 and k4 1.0.
 58. A nozzle as in claim 50 wherein k3 < k1 k4 <0 k1 and k4 < k2.
 59. A nozzle as in claim 58 wherein k1 2 k2 100 k3 0.001 and k4 1.0.
 60. A nozzle as in claim 42 wherein a depressed groove portion is formed between the terminus of the curve of the orifice lower surface and the beginning of the conical surface.
 61. A nozzle for spraying a fluid comprising body means formed within an inlet passage for receiving the fluid to be sprayed and a bore, means forming a swirl chamber having a portion which is in the shape of an arc of a curve, said swirl chamber having an inlet opening for communication with said bore, and means forming a generally circular orifice having an outlet in communication with said swirl chamber, the lower surface of said orifice forming means having the shape of a portion of an arc of a curve starting from a point at the top plane of the swirl chamber and extending upwardly to form the nozzle outlet, the outer surface of the orifice tapering outwardly in a generally conical shape above the terminus of the curve of the orifice lower surface, the height of the orifice forming means from the upper plane of the swirl chamber to the terminus of the curved portion being L, and the radius of the curved portion being r, with r1 being less than L.
 62. A nozzle as in claim 61 wherein the surface from the top plane of the swirl chamber to the beginning of the conical surface is fully curved and has two different radii. The distance from the junction of the two radii and the upper plane of the swirl chamber being L, said portion of the curve surface included in the distance L having a radius r, and the portion of the surface from the junction of the two radii to the beginning of the conical surface being r2.
 63. A nozzle for spraying a fluid comprising body means formed with an inlet passage for receiving the fluid to be sprayed and a bore, means forming a swirl chamber having at least a portion which is in the shape of a circle, said swirl chamber having an inlet opening for communication with said bore, and means forming an orifice having an outlet in communication with said swirl chamber, said nozzle having at a reference pressure drop Delta Pref an actual flow rate Qref which is related to Dor2, B.H (nozzle inlet area) and Rsc by the relationship: log Qref b4 log Dor2 + b5 log BH + b6 log Rsc + KQ 1 and a spray angle (2 psi ) in degrees which is related to D2 or, B, H and Rsc by another relationship: log 2 psi ref a5 log (BH/Dor2) + a6 log Rsc + a7 log H+a8 log B+K2
 2. where Qref is the weight flow rate at the reference pressure drop; Dor is the diameter of orifice means outlet; B is the width of the tangential inlet close to the inlet opening of the swirl chamber; H is the height of the swirl chamber; Rsc is the largest radius of the swirl chamber; 2 psi ref is the spray cone angle at the refeRence pressure drop; Delta Pref is the reference pressure drop of the nozzle; and: where b4 through b6, a5 through a8, K and K2 are the real number constants.
 64. A nozzle as in claim 63 wherein the actual flow rate (Q) at a given pressure drop ( Delta P) is related to the actual flow rate at the reference pressure drop (Qref) by: Q Qref Square Root Delta P/ Delta Pref.
 65. A nozzle as in claim 63 in which the patternation index deltaref at the reference pressure drop Delta Pref is described and predicted as follows: log delta (delta)ref c6 log (LBH3/RscDor4) + c7(B/Dor) + c8 (H/Dor) + c9 (B2/D2or) +c10 (Rsc2/D2or) + K where c6 through c10 and K are real number constants; deltaref is the patternation index delta at the reference pressure drop; and L is the thickness of the orifice means at its outlet.
 66. A nozzle as in claim 65, wherein the actual flow rate (Q) at a given pressure drop ( Delta P) is related to the actual flow rate at the reference pressure drop (Qref) by: Q Qref Square Root Delta P/ Delta Pref. 